Research On Dimension Reduction Algorithm Based On Manifold Learning And Its Application To Face Recognition

Human face is the most common visual part. Human face recognition has become notonly a hot research topic in the field of artificial intelligence and model recognition,but also amost potential recognition technology by biometric characteristic for the merits of beingnatural, directly perceived, safe and convenient. For high-dimensional data, extraction ofeffective features is important for pattern recognition. The biological characteristics of facerecognition, image dimensionality reduction (feature extraction) is a very important aspect offace recognition. Manifold learning based face recognition methods have attractedconsiderable interests in recent years. It has archived remarkable success in datadimensionality reduction. In this thesis, we introduce the graph embedding and analyzes someclassical algorithms firstly.Then, this article is intended to improve the manifold learningalgorithms for dimensionality reduction and feature extraction, and to apply them to the facerecognition problem. The efficiency of the proposed algorithms is demonstrated by extensiveexperiments in face database and comparison with other algorithms. The main work in thefollowing areas:(1)In order to address Small Sample Size (SSS) problem encountered by NeighbourhoodPreserving Discriminant Embedding (NPDE) and make full use of the discriminant informa-tion in the null space and non-null space of within-neighbourhood scatter matrix for facerecognition， this paper proposed a Complete Orthogonal Neighbourhood PreservingDiscriminant Embedding (CONPDE) algorithm for face recognition.The algorithm firstlyremoved the null space of the total neighbourhood scatter matrix using eigen decompositionmethod indirectly. Then,the optimal discriminant vectors were extracted in the null space andnon-null space of within-neighbourhood scatter matrix, respectively. Besides, to furtherimprove the recognition performance, the orthogonal projection matrix obtained based oneconomic QR decomposition was given. Extensive experiments in ORL and Yale facedatabase show the efficiency of the proposed method.(2)The dimensionality reduction by orthogonal projection techniques helped preserve theinformation related to the metric structure and improved the recognition performance in facerecognition. Based on spectral regression discriminant analysis (SRDA) and spectral regres-sion kernel discriminant analysis (SRKDA), this paper proposed two dimensionality reductionalgorithms named orthogonal SRDA (OSRDA) and orthogonal OSRKDA (OSRKDA).Firstly,a set of orthogonal discriminant vectors obtained based on cholesky decomposition was given.Then, this paper orthogonalized the projection vectors of SRDA and SRKDA by thismethod.It was very simple and easy to implement. What’s more,it overcame the shortcomingthat the iterative algorithm of orthogonal discriminant vectors was not suitable for spectralregression dimensionality reduction algorithms.Experiments on ORL、 Yale and PIEdemonstrate the effectiveness and efficiency of the algorithms,and show that these algorithmscan reduce the dimensions of the data and improve the discriminant ability.(3)Null-space linear discriminant analysis (NLDA) shows desirable performance,but it isstill a linear technique in nature. In order to effectively extract nonlinear features of data set，a novel null-space kernel discriminant analysis (NKDA) is proposed for face recognition. First,the kernel function is used to project the original samples into an implicit space called featurespace by nonlinear kernel mapping. Then,the discriminant vectors in the null space of thekernel within-scatter matrix are extracted by only one step of economic QRdecomposition.Finally, one step of Cholesky decomposition is used to obtain the orthogonaldiscriminant vectors in the kernel space. Compared with NLDA,not only does NKDA achievebetter performance,but it is applicable to the large sample size problem.Besides, based onNKDA,the incremental NKDA method is developed,which can accurately update thediscriminant vectors of NKDA when new samples are inserted into the training set.Experiments on ORL、Yale face database,and PIE subset demonstrate the effectiveness andefficiency of the algorithms,and show that the algorithm can reduce the dimensions of the dataand improve the discriminant ability.